Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multi-Harmonic Frequency Responses

• In industry, linear FE-models commonly serve as baseline models to represent the global structural dynamics behavior. However, available test data may show evidence of significant nonlinear dynamic characteristics. In such a case, the baseline linear model may be insufficient to represent the dynamics of the structure. The causes of the nonlinear characteristics may be local in nature and the remaining parts of the structure may be satisfactorily represented by linear descriptions. Although the baseline model can then serve as a good foundation, the physical phenomena needed to substantially increase the model's capability of representing the real structure are most likely not modelled in it. Therefore, a set of candidate nonlinear property parameters to control the nonlinear effects have to be added and subjected to calibration to form a credible model. The selection of the calibration parameters and the choice of data for a calibration metric form a coupled problem. An over-parameterized model for calibration may result in parameter value estimates that do not survive a validation test. The parameterization is coupled to the test data and should be chosen so that the expected co-variances of the chosen parameter's estimates are made small. Accurate test data, suitable for calibration, is often obtained from sinusoidal testing. Because a pure mono-sinusoidal excitation is difficult to achieve during a test of a nonlinear structure, the excitation is here designed to contain sub and super harmonics besides the fundamental harmonic. The steady-state responses at the side frequencies are shown to contain valuable information for the calibration process that can improve the accuracy of the parameter estimates. The nonlinear steady-state solutions can be found efficiently using the multi-harmonic balance method. In this paper, synthetic test data from a model of a nonlinear benchmark structure are used for illustration. The model calibration and an associated K-fold cross-validation are based on the Levenberg-Marquardt and the undamped Gauss-Newton algorithm, respectively. Starting seed candidates for calibration are found by the Latin hypercube sampling method. The realization that gives the smallest deviation to test data is selected as a starting point for the iterative search for a calibration solution. The calibration result shows good agreement with the true parameter setting, and the K-fold cross validation result shows that the variance of the estimated parameters shrinks when adding sub and super harmonics to the nonlinear frequency response functions.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering (hsv//eng)

Nyckelord

model calibration

Fisher information matrix

identifiability

multi-harmonic response

cross-validation

Mechanical Engineering

Maskinteknik

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